A= {a,b,c,d,e} .find the total number of subsets of set A
Answers
A subset of a set is the same thing as choosing which elements from your original set you are going to keep, and which ones that you do not.
So if you have a set with n elements then there are 2n possible subsets.
For the given set A={a,b,c,d} there are 4 elements so there are 24=16 possible subsets.
I can list them out with the corresponding binary representation
0000,0001,0010,0011,0100,0101,0110,0111
1000,1001,1010,1011,1100,1101,1110,1111
{},{a},{b},{a,b},{c},{a,c},{b,c},{a,b,c}
{d},{a,d},{b,d},{a,b,d},{c,d},{a,c,d},{b,c,d},{a,b,c,d}
The set of subsets is called the power set.
|P(X)|=2|X|
This works even for infinite sets. We call the cardinality of the natural numbers ℵ0 , so the cardinality of the power set of the natural numbers would be 2ℵ0 .
Step-by-step explanation:
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